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This work will cover the problems that are found in teacher training and professional development in Probability and Statistics in higher education in Mexico. It will be approached through four focuses: a) the characterization and training of teachers that drive the development and implementation of curriculum reforms in the teaching of Statistics; b) challenges of teachers in the instruction of university-level Statistics; c) new curricular reforms with respect to the instruction of Statistics that propose the development of a learning based in projects through the use of appropriate statistical software, and d) educational innovation as a body of knowledge in development, by which the shaping of networks consisting of professors who favor the emergence of real innovation is brought about. Starting from these perspectives, the challenges confronted in the teaching and training of Statistics professors will be proposed.